Summary Mathematical Functions: Concepts, Properties, and Applications

Functions – General Mathematics Notes



1. Introduction to Functions

- A function is a relation where each input (x) has exactly one output (y).

- Functions are commonly written as f(x), meaning “f of x.”

- Example: f(x) = 2x + 3

- If x = 2, then f(2) = 2(2) + 3 = 7



2. Definition of a Function

- A function is a rule that assigns each element in the domain (input) to
exactly one element in the range (output).

- Notation: f: X → Y, meaning f is a function from set X to set Y.



Example of a function:

F(x) = x^2 + 1

Domain (Input values): {1, 2, 3}

Range (Output values): {2, 5, 10}



3. Domain and Range of a Function

- Domain: The set of all possible input values (x-values).

- Range: The set of all possible output values (y-values).



Example:

For f(x) = √(x – 1)

- The domain is x ≥ 1 (because we cannot take the square root of a negative
number).

- The range is y ≥ 0.